Analyzing Dataset with Noise in Geometric Fashion

We represent that the relevant information in a supervised scenario is contained in the projected kernel PCA components if the kernel is sufficiently smooth. This behavior complements the common statistical learning theoretical view on kernel based learning adding insight on the intricate interplay of data and kernel. Thus, kernels do not only transform data sets such that good generalization can be achieved using only linear discriminant functions, but this transformation is also performed in a manner which makes economical use of feature space dimensions. We propose an algorithm which can be applied to denoise in feature space and analyze the interplay of data set and kernel in a geometric fashion.